drive the expression for magnetic field due to toroid
Answers
If a solenoid is bent in a circular shape and the ends are joined, we get a toroid. Alternatively, one can start with a nonconducting ring and wind a conducting wire closely on it. The magnetic field in such a toroid can be obtained using Ampere's Law.
MAGNETIC FIELD DUE TO A TOROID - EXAMPLE
concept
The magnetic field in the open space inside (point P) and exterior to the toroid (point Q) is zero. The field B inside the toroid is constant in magnitude for the ideal toroid of closely wound turns.The direction of the magnetic field inside is clockwise as per the right-hand thumb rule for circular loops. Three circular Amperian loops 1, 2 and 3 are shown by dashed lines. By symmetry, the magnetic field should be tangential to each of them and constant in magnitude for a given loop.
Example:The number of turns per unit length in a toroid is 10
3 and current flowing in it is
4π1 ampere, then the magnetic induction produced in it, is :
Magnetic field in a toroid B=μ
0 nGiven n=10
and i= 4π1 A
We know that μ
0 =4π×10 −7
T/AB
=4π×10 −7 ×10 3 × 4π1
=10 −4
T
NUMBER OF TURNS IN A TOROIDAL COIL - FORMULA
concept
The figure below shows a cross-sectional view of the inner radius of a toroid inductor and wire. The inner radius of the torus is A, the radius of the wire is r, and the maximum number of loops is n.
The equation that relates A, r, and n is:
sin( nπ )=
A−r
r in radians
n= arcsin A−rπ
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